Moving a broody, especially a first timer, is always a bit touchy. Some birds move with ease; others fight it and return to the original nest abandoning the eggs. In unsure situations, I leave the hen in the nest if it is safe for the hen and she is free from intruders; otherwise, it is better to risk moving her.
I have set up a partition around a hen who insisted on nesting in the main box, so sometimes that is the best avenue.
She can hatch from a higher nest, just move the babies after they hatch on their first day. Mom will likely be moving them then anyway as she'll know they can't get into the nest from the ground. I've had great success with moving broodies with their freshly hatched babies (make sure all are hatched and dry).
You may have some staggering since you set yesterday and today...but likely not much. I would not recommend adding anymore eggs as you don't want a significantly staggered hatch especially if you plan to move the hen from the high nest after the babies dry.
As to "effortlessly" adding them all in for integration...I'm not sure what you mean....adding them all at once in one pen to grow up together? Adding the incubator chicks to the EE with her babies? Adding them to the flock with mom EE? That would be a LOT of chicks for a hen to try to take care of, especially a first time hen.
I've also personally had issues with adding multiple age chicks in a mixed situation (chicks hatched by a broody and then adding fosters from the store which are of course incubated then brooded by a heat lamp)...the hatchlings tend to trample the fosters as they are especially vigorous being used to being hen brooded. Also there is a big difference in one week with chick ages...week olds run around a lot more and mom might find them intruders and try to protect her chicks. Some hens welcome everybody, others not so much. The older ones can trample the younger ones in that instance.
I guess to sum it up...I personally prefer mom to brood as it saves on stress and trouble with integration...but that would be a lot of chicks for one hen, of mixed ages. Adding a heat lamp, if it is safe to do so, can help, but will introduce some integration issues with the environment as the chicks will need to be weaned off the heat lamp, but it may be the best direction for you with that many unless you keep the two broods separate...let mom do her thing with the hatchlings and brood the incubator chicks as you normally would integrating after they have fully feathered around 6 to 8 weeks, depending on your pens. From my experience (failures) in mixing fosters with hatchlings, especially of week or more age differences, I'd keep them separate.
Lady of McCamley